A short pdf on airfoils,
https://www.nasa.gov/sites/default/files/atoms/files/hallion.pdf
Why did the Germans use NACA airfoils when they had their own airfoil designs, Gottingen?
The Gottingen airfoils were extremely significant.
If you look at wing profiles from Otto Lillienthal through to the Wright brother to ALL allied fighter aircraft through world war one you will notice that they are only
4% thick, slimmer than a supersonic fighter.
The Germans were the first to realize that thick airfoils
(greater than 10%) are much better. They had nearly twice the lift coefficient of thin sections. They were used on the Fokker Triplane and Fokker DVIII and so these aircraft and so these aircraft had much higher climb rates and smaller turning circles than allied aircraft. The fighters the Germans were about to produce just before the armistice would have trounced any allied fighter.
What had happened is this. Hugo Junkers was inspired to develop all metal monoplanes. He didn't like the idea of struts and braces holding the wings up so he investigated thick airfoils that were thick enough to carry the big strong spars needed.
The results delighted him and Junkers built no only the first all metal aircraft but the first unbraced monoplane.
Anthony Fokker essentially stole the Junkers information and ideas and the rest his history.
The AVA at Gottingen had Betz and Prandle (who had developed the boundary layer and lifting line theory) understood what had happened straight away.
Wing sections were being tested subscale. However because of Reynold effects the boundary layer is different. Put it this way, if boundary layer is laminar for 1cm then it is laminar across a bees wing which can be very thin and flat. However 1cm across a sub scaled model is maybe 10% but is insignicant on a full wing.
The Gottingehn series were thus the first modern airfoils. They were widely copied until the NACA series took overs as a resutt of the NACA massive investment.
German researchers were moving on to swept wings, laminar flow wings, boundary layer suction (flown on test beds) which would have been used on the second generation of German jets. Its really a matter of timing the Germans didn't get a laminar flow wing in service though it can be argued the sections used on the Me 262 and Ar 234 were exactly that.